Simplify the following expression: $\dfrac{72x^5}{54x^2}$ You can assume $x \neq 0$.
Solution: $ \dfrac{72x^5}{54x^2} = \dfrac{72}{54} \cdot \dfrac{x^5}{x^2} $ To simplify $\frac{72}{54}$ , find the greatest common factor (GCD) of $72$ and $54$ $72 = 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3$ $54 = 2 \cdot 3 \cdot 3 \cdot 3$ $ \mbox{GCD}(72, 54) = 2 \cdot 3 \cdot 3 = 18 $ $ \dfrac{72}{54} \cdot \dfrac{x^5}{x^2} = \dfrac{18 \cdot 4}{18 \cdot 3} \cdot \dfrac{x^5}{x^2} $ $\phantom{ \dfrac{72}{54} \cdot \dfrac{5}{2}} = \dfrac{4}{3} \cdot \dfrac{x^5}{x^2} $ $ \dfrac{x^5}{x^2} = \dfrac{x \cdot x \cdot x \cdot x \cdot x}{x \cdot x} = x^3 $ $ \dfrac{4}{3} \cdot x^3 = \dfrac{4x^3}{3} $